mypy: enable allow-redefinition-new and fix fallout

Reduces 3 errors that show up in newer mypy versions than pinned in CI.

It is new since 1.16 and a likely future default for mypy 2.0. It allows
things like:

```
for i in ['one', 'two', 'three']:
    frob_a(i)

for i in [1, 2, 3]:
    frob_b(i)
```

since "i" is obviously used as a loop holder and its type can be freely
reinvented. Note: allow-redefinition-new isn't actually about this at
all, it has greater scope than loop holders and allows redefining
"unannotated variables" of all kinds. No granularity in what to accept
redefinition of. :P

To enable this, we must also opt in to local-partial-types, which has
some overlap with None-safety. Specifically:

> the most common cases for partial types are variables initialized
> using None, but without explicit X | None annotations. By default, mypy
> won’t check partial types spanning module top level or class top level.
> This flag changes the behavior to only allow partial types at local
> level, therefore it disallows inferring variable type for None from two
> assignments in different scopes.

So with this, we also fix a couple of actual type errors this revealed.
Where possible, stop None-initializing at all -- it's not strictly
needed for global variables, anyway, and it's a coding error if it is
possible to hit these variables without defining them first.

Bug: https://github.com/python/mypy/issues/19280

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